Solve (31/4+23/8-31/16)div(41/2-frac{5}{8})

$$( 3 \frac { 1 } { 4 } + 2 \frac { 3 } { 8 } - \frac { 31 } { 16 } ) \div ( 4 \frac { 1 } { 2 } - \frac { 5 } { 8 } )$$

Evaluate

$$\frac{59}{62}\approx 0.951612903$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{12+1}{4}+\frac{2\times 8+3}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{4}+\frac{2\times 8+3}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Multiply 2 and 8 to get 16.

$$\frac{\frac{13}{4}+\frac{16+3}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Add 16 and 3 to get 19.

$$\frac{\frac{13}{4}+\frac{19}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{13}{4} and \frac{19}{8} to fractions with denominator 8.

$$\frac{\frac{26}{8}+\frac{19}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Since \frac{26}{8} and \frac{19}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{26+19}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Add 26 and 19 to get 45.

$$\frac{\frac{45}{8}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Least common multiple of 8 and 16 is 16. Convert \frac{45}{8} and \frac{31}{16} to fractions with denominator 16.

$$\frac{\frac{90}{16}-\frac{31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Since \frac{90}{16} and \frac{31}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{90-31}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Subtract 31 from 90 to get 59.

$$\frac{\frac{59}{16}}{\frac{4\times 2+1}{2}-\frac{5}{8}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{59}{16}}{\frac{8+1}{2}-\frac{5}{8}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{59}{16}}{\frac{9}{2}-\frac{5}{8}}$$

Least common multiple of 2 and 8 is 8. Convert \frac{9}{2} and \frac{5}{8} to fractions with denominator 8.

$$\frac{\frac{59}{16}}{\frac{36}{8}-\frac{5}{8}}$$

Since \frac{36}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{59}{16}}{\frac{36-5}{8}}$$

Subtract 5 from 36 to get 31.

$$\frac{\frac{59}{16}}{\frac{31}{8}}$$

Divide \frac{59}{16} by \frac{31}{8} by multiplying \frac{59}{16} by the reciprocal of \frac{31}{8}.

$$\frac{59}{16}\times \frac{8}{31}$$

Multiply \frac{59}{16} times \frac{8}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{59\times 8}{16\times 31}$$

Do the multiplications in the fraction \frac{59\times 8}{16\times 31}.

$$\frac{472}{496}$$

Reduce the fraction \frac{472}{496} to lowest terms by extracting and canceling out 8.

$$\frac{59}{62}$$

Factor

$$\frac{59}{2 \cdot 31} = 0.9516129032258065$$